It was a fundamental rule, for instance, that two negative premises could give no conclusion. If we take the propositions Granite is not a sedimentary rock, (1) Basalt is not a sedimentary rock, (2) we ought not to be able to draw any inference concerning the relation between granite and basalt. Taking our letter-terms thus: A = granite, B = sedimentary rock, C = basalt, the premises may be expressed in the forms A ~ B, (1) C ~ B. (2) We have in this form two statements of difference; but the principle of inference can only work with a statement of agreement or identity (p. 63). Thus our rule gives us no power whatever of drawing any inference; this is exactly in accordance with the fifth rule of the syllogism. It is to be remembered, indeed, that we claim the power of always turning a negative proposition into an affirmative one (p. 45); and it might seem that the old rule against negative premises would thus be circumvented. Let us try. The premises (1) and (2) when affirmatively stated take the forms A = A*b* (1) C = C*b*. (2) The reader will find it impossible by the rule of substitution to discover a relation between A and C. Three terms occur in the above premises, namely A, *b*, and C; but they are so combined that no term occurring in one has its exact equivalent stated in the other. No substitution can therefore be made, and the principle of the fifth rule of the syllogism holds true. Fallacy is impossible. It would be a mistake, however, to suppose that the mere occurrence of negative terms in both premises of a syllogism renders them incapable of yielding a conclusion. The old rule informed us that from two negative premises no conclusion could be drawn, but it is a fact that the rule in this bare form does not hold universally true; and I am not aware that any precise explanation has been given of the conditions under which it is or is not imperative. Consider the following example: Whatever is not metallic is not capable of powerful magnetic influence, (1) Carbon is not metallic, (2) Therefore, carbon is not capable of powerful magnetic influence. (3) Here we have two distinctly negative premises (1) and (2), and yet they yield a perfectly valid negative conclusion (3). The syllogistic rule is actually falsified in its bare and general statement. In this and many other cases we can convert the propositions into affirmative ones which will yield a conclusion by substitution without any difficulty. To show this let A = carbon, B = metallic, C = capable of powerful magnetic influence. The premises readily take the forms *b* = *bc*, (1) A = A*b*, (2) and substitution for *b* in (2) by means of (1) gives the conclusion A = A*bc*. (3)